By default, I don't think that this is possible. One thing that we could do though, is create custom fields that show this information. One example would be the 'Date Time' custom field, that would show both the date and time in its field values.
I've tested this, and it would show both the date and time in the Issue Navigator (without requiring the cursor to hover above it). However, you would have to manually enter the values for this custom field, as they would not be automatically filled.
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